Report on the German credit dataset
Elodie Kwan and Katia Voltz
2022-05-20
Executive Summary
Data analysis is now a fundamental tool in the general understanding of business. In the current case, the objective would be to understand and profile the different historical and current customers of a bank, in order to better identify them. For this, we need to proceed in several steps: The first is to collect available data, check its relevance and see if it is accurate. Indeed, it is possible to deal with erroneous data. Therefore, it is necessary to check each feature and instance collected. The second step is to clean and understand the data in order to proceed to a more complete analysis. Finally, the goal is to answer the problem by using different analytical methods and synthesising the best model to provide a solution.
Introduction
In the bank industry many bankers have to decid whether or not they should issue a loan to a new coming applicant. In this report, we will use the data set called German Credit data which was given to us.
The German credit data set contains 1000 observations of past credit applicants, described by 30 variables. The applicants are described as Good Credit risk or Bad Credit risk: Therefore, the response variable, studied, is the credit rating.
Response variable: RESPONSE in the dataset:
- 0 : Bad credit. In case of bad credit, the banker would not want to issue loan to this person.
- 1 : Good credit. In case of good credit, the banker will want to issue loan to this applicant as it is more likely that the company will benefit from it.
All the other observations are features of the applicants that are going to be studied. It will allow us to perform several machine learning models and deploy a CRISP-DM model to come up with the best classifying model with the highest accuracy as possible. We want to determine whether the new applicant has a ‘Good’ credit risk, in which case the loan should be issued, or a ‘Bad’ credit risk, in which case it is not advisable to give him a loan.
The tasks required to perform our analysis is stated as follow.
1/ We first proceeded to some data cleaning, meaning that we sorted the dataset to make it ready for the analysis.
2/ Then we followed by an exploratory data analysis (EDA) where we studied the dataset and the different variables, one by one, and we made an principal component analysis.
3/ Next, came the models analysis, the steps are listed below:
- Splitting the dataset
- Balancing the data
- Fitting the models
- Accuracy study (scoring)
- Variable selection and importance
- Cross-validation / Bootstrap
- Final Best model
Our very first steps once we received the German Credit data was to dig into it and get to know the observations and features we were going to work with.
Get to know the data
The title of the dataset is German credit data and the name of the file is GermanCredit.cvs.
As said in the introduction, the German Credit data has data on 1000 observations on past credit applicants and it is described by 30 attributes. Each applicant is rated as “Good” or “Bad” credit (encoded as 1 and 0 respectively in the RESPONSE variable). The definitions of all the attributes are stated in the annex under ‘Appendix A’.
We looked at the attribute Information :
| OBS. | CHK_ACCT | DURATION | HISTORY | NEW_CAR | USED_CAR | FURNITURE | RADIO.TV | EDUCATION |
|---|---|---|---|---|---|---|---|---|
| Min. : 1.0 | Min. :0.000 | Min. : 4.0 | Min. :0.000 | Min. :0.000 | Min. :0.000 | Min. :0.000 | Min. :0.00 | Min. :-1.000 |
| 1st Qu.: 250.8 | 1st Qu.:0.000 | 1st Qu.:12.0 | 1st Qu.:2.000 | 1st Qu.:0.000 | 1st Qu.:0.000 | 1st Qu.:0.000 | 1st Qu.:0.00 | 1st Qu.: 0.000 |
| Median : 500.5 | Median :1.000 | Median :18.0 | Median :2.000 | Median :0.000 | Median :0.000 | Median :0.000 | Median :0.00 | Median : 0.000 |
| Mean : 500.5 | Mean :1.577 | Mean :20.9 | Mean :2.545 | Mean :0.234 | Mean :0.103 | Mean :0.181 | Mean :0.28 | Mean : 0.048 |
| 3rd Qu.: 750.2 | 3rd Qu.:3.000 | 3rd Qu.:24.0 | 3rd Qu.:4.000 | 3rd Qu.:0.000 | 3rd Qu.:0.000 | 3rd Qu.:0.000 | 3rd Qu.:1.00 | 3rd Qu.: 0.000 |
| Max. :1000.0 | Max. :3.000 | Max. :72.0 | Max. :4.000 | Max. :1.000 | Max. :1.000 | Max. :1.000 | Max. :1.00 | Max. : 1.000 |
| RETRAINING | AMOUNT | SAV_ACCT | EMPLOYMENT | INSTALL_RATE | MALE_DIV | MALE_SINGLE | MALE_MAR_or_WID | CO.APPLICANT |
|---|---|---|---|---|---|---|---|---|
| Min. :0.000 | Min. : 250 | Min. :0.000 | Min. :0.000 | Min. :1.000 | Min. :0.00 | Min. :0.000 | Min. :0.000 | Min. :0.000 |
| 1st Qu.:0.000 | 1st Qu.: 1366 | 1st Qu.:0.000 | 1st Qu.:2.000 | 1st Qu.:2.000 | 1st Qu.:0.00 | 1st Qu.:0.000 | 1st Qu.:0.000 | 1st Qu.:0.000 |
| Median :0.000 | Median : 2320 | Median :0.000 | Median :2.000 | Median :3.000 | Median :0.00 | Median :1.000 | Median :0.000 | Median :0.000 |
| Mean :0.097 | Mean : 3271 | Mean :1.105 | Mean :2.384 | Mean :2.973 | Mean :0.05 | Mean :0.548 | Mean :0.092 | Mean :0.041 |
| 3rd Qu.:0.000 | 3rd Qu.: 3972 | 3rd Qu.:2.000 | 3rd Qu.:4.000 | 3rd Qu.:4.000 | 3rd Qu.:0.00 | 3rd Qu.:1.000 | 3rd Qu.:0.000 | 3rd Qu.:0.000 |
| Max. :1.000 | Max. :18424 | Max. :4.000 | Max. :4.000 | Max. :4.000 | Max. :1.00 | Max. :1.000 | Max. :1.000 | Max. :1.000 |
| GUARANTOR | PRESENT_RESIDENT | REAL_ESTATE | PROP_UNKN_NONE | AGE | OTHER_INSTALL | RENT | OWN_RES | NUM_CREDITS |
|---|---|---|---|---|---|---|---|---|
| Min. :0.000 | Min. :1.000 | Min. :0.000 | Min. :0.000 | Min. : 19.0 | Min. :0.000 | Min. :0.000 | Min. :0.000 | Min. :1.000 |
| 1st Qu.:0.000 | 1st Qu.:2.000 | 1st Qu.:0.000 | 1st Qu.:0.000 | 1st Qu.: 27.0 | 1st Qu.:0.000 | 1st Qu.:0.000 | 1st Qu.:0.000 | 1st Qu.:1.000 |
| Median :0.000 | Median :3.000 | Median :0.000 | Median :0.000 | Median : 33.0 | Median :0.000 | Median :0.000 | Median :1.000 | Median :1.000 |
| Mean :0.053 | Mean :2.845 | Mean :0.282 | Mean :0.154 | Mean : 35.6 | Mean :0.186 | Mean :0.179 | Mean :0.713 | Mean :1.407 |
| 3rd Qu.:0.000 | 3rd Qu.:4.000 | 3rd Qu.:1.000 | 3rd Qu.:0.000 | 3rd Qu.: 42.0 | 3rd Qu.:0.000 | 3rd Qu.:0.000 | 3rd Qu.:1.000 | 3rd Qu.:2.000 |
| Max. :2.000 | Max. :4.000 | Max. :1.000 | Max. :1.000 | Max. :125.0 | Max. :1.000 | Max. :1.000 | Max. :1.000 | Max. :4.000 |
| JOB | NUM_DEPENDENTS | TELEPHONE | FOREIGN | RESPONSE |
|---|---|---|---|---|
| Min. :0.000 | Min. :1.000 | Min. :0.000 | Min. :0.000 | Min. :0.0 |
| 1st Qu.:2.000 | 1st Qu.:1.000 | 1st Qu.:0.000 | 1st Qu.:0.000 | 1st Qu.:0.0 |
| Median :2.000 | Median :1.000 | Median :0.000 | Median :0.000 | Median :1.0 |
| Mean :1.904 | Mean :1.155 | Mean :0.404 | Mean :0.037 | Mean :0.7 |
| 3rd Qu.:2.000 | 3rd Qu.:1.000 | 3rd Qu.:1.000 | 3rd Qu.:0.000 | 3rd Qu.:1.0 |
| Max. :3.000 | Max. :2.000 | Max. :1.000 | Max. :1.000 | Max. :1.0 |
We noticed that the variable EDUCATION has a minimum value of ‘-1’ but it should be ‘0’ since there are only 2 levels (0 and 1). Indeed, the observation 37 indicate a value of ‘-1’ for EDUCATION. We notice another strange value, in the variable GUARANTOR, the maximum value is of ‘2’ while it does not mean anything in our data set.
After discussion with the Banker, he gave us the correct values to these 2 mistakes. Observation 37 of EDUCATION and observation 234 of GUARANTOR should be equal to 1. We corrected these two values.
We also saw that the variable AGE has a maximum of 125. This is strange because it is very unlikely that someone lives to the age of 125. We talked to the banker again and he confirmed our doubts by telling us that a mistake has been made. At the observation 537, the correct age of the client is 75 years old. He asked us to correct this value in our data set.
After looking at the different attributes, we concluded that there were no missing values.
The response variable is identified as being the column named ‘Response’ and it apprears to be the last column on the data.
It is a dummy variable with 0/1.
- 0 : No, the credit rating is bad.
- 1 : Yes, the credit rating is good.
We had to make sure that the class of the variables are correct. First when we imported the data, all the variables were defined as integer but we know that we should have numerical and categorical variables in our dataset. Therefore, we transformed the class of some of them.
The binomial and categorical data are set as factors and the others as numerical.
We then described the variables one more time with the function
describe from the Hmisc package because we
should get better results as our computer now recognizes the factor
variables and the numerical ones.
| rows | columns | discrete_columns | continuous_columns | all_missing_columns |
|---|---|---|---|---|
| 1000 | 32 | 26 | 6 | 0 |
| total_missing_values | complete_rows | total_observations | memory_usage |
|---|---|---|---|
| 0 | 1000 | 32000 | 237424 |
The plot helps us to see the percentage of continuous variable, the percentage of discrete variables and whether or not some observations are missing. Here it states that we have 81% of discrete columns and 19% of continuous one.
Visualization of the data
First, we plot all the continuous variables into histograms and their corresponding density plots.
Our first notice is that the data are not really normally distributed. Some of them are right-tailed.
We can look at the tails and outliers more in deep through boxplots.
This seems not to be disturbing. It makes sense that only a few people has a big credit amount. However it seems that the ‘bad’ clients tends to ask for bigger credit amount than ‘good’ clients.
Then, we made some barplots of the categorical variables (appendix B).
From these barplots we saw:
- The majority of people do not check their account status. (CHK_ACCT)
- Most people have an average balance of less than < 100 DM in their saving account. (SAV_ACCT)
- Most of the applicants has its own residence. (OWN_RES)
- Almost none of the applicants is a foreign worker. (FOREIGN)
- We have more information on people that are ‘good’ applicants and less information on ‘bad’ applicants. It would be better to have more information on ‘bad’ applicants as well in order to make good predictions with models. We will have to take this into account later. (RESPONSE)
To wrap up, we looked at a general summary of the data with the
command dfSummary to make sure that the right class was
applied to the columns, and to see their distribution and frequency
(Appendix C). We concluded that our data were well structured.
Correlation Analysis :
Correlation plot between continuous variables :
There are little correlation between the continuous variables. We can notice that there is a correlation of 62% between the variable DURATION and AMOUNT. This makes sense and is known by the bankers that the bigger the amount of credit, the longer the duration of the credit in months will last.
Correlation plot between categorical variables :
It is difficult to look at the correlation since there are a lot of variables on the graph. We can still see higher correlation between RESPONSE 1:
- and people that do not check their account (CHK_ACCT_3)
- and people that have a critical historical account (HISTORY_4)
- and the variable REAL_ESTATE (REAL_ESTATE)
- and applicant that does not have their own property (PROP_UNKN_NONE_0)
- and applicant that have their own residence (OWN_RES_1)
We can also see some correlation between RESPONSE 0:
- and people that have a checking account status < 0 DM (CHK_ACCT_0)
- and people that have an average balance in savings account < 100 DM (SAV_ACCT_0)
- and the variable REAL_ESTATE (REAL_ESTATE)
Principal Component Analysis Exploration:
It is good to perform a PCA Exploration in order to reduce the dimensions or/and see which variables to select.
We start by selecting the numerical values because the PCA only works on numerical variables.
## Importance of components:
## PC1 PC2 PC3 PC4 PC5 PC6
## Standard deviation 1.2873 1.1208 1.0443 0.9318 0.9193 0.53164
## Proportion of Variance 0.2762 0.2094 0.1818 0.1447 0.1409 0.04711
## Cumulative Proportion 0.2762 0.4856 0.6673 0.8120 0.9529 1.00000From the PCA summary we can see 4 principal components should be taken into account in order to explain approximately 81% of the variation of the data.
Eigenvalue analysis:
## eigenvalue variance.percent cumulative.variance.percent
## Dim.1 1.6570953 27.618256 27.61826
## Dim.2 1.2562810 20.938016 48.55627
## Dim.3 1.0906419 18.177365 66.73364
## Dim.4 0.8682109 14.470181 81.20382
## Dim.5 0.8451277 14.085462 95.28928
## Dim.6 0.2826431 4.710719 100.00000Then from this eigenvalues table, we know that we need to choose 3 dimensions because the first 3 dimensions are higher than the value 1.
From this circle of correlations, we see that :
- The first principal component PC1 is strongly positively correlated
with the variables AMOUNT and
DURATION. So the larger PC1, the larger these features.
It is also a little bit negatively correlated with
INSTALL_RATE.
- The second principal component PC2 is strongly positively correlated with AGE, NUM_DEPENDENTS and NUM_CREDITS.
From the below biplot, we can see some characteristics of the observations.
Here, we see the distribution of the response variables (0-1) according to the reduced dimension. What we can observe, is that the “Bad credits: 0”, look a little bit more positively correlated to dimension 1. Therefore, more correlated to Amount and Duration. Compared to Good Credits, it looks positively correlated to dimension 2; AGE, NUM_CREDITS, NUM_DEPENDENTS.
After having cleaned the dataset and looked at all the different features, we created a new dataset, named GermandCredit_cleaned.csv, that contains our modifications in order to use it for our analysis.
Methodology
In this section we will talk about the methodology that has been used and the different models analysis that has been conducted.
Traning set and Test set
First of all we started by splitting our dataset into 2 sets:
training set (German_credit.tr) and
test set (German_credit.te). We do not
forget to take the first variable OBS. out as it
represents the index number for each observation. These two sets will
allow us to train some models on the training set and
then test the accuracy of the model fit on the test
set.
Balancing the dataset
Then, we applied the balancing data technique in order to improve the predictions of Good Credit and Bad Credit, since we have more observations on the Good Credit.
The table below reveals the unbalanced problem.
Indeed, we observe that the “Good Credit” (1) response appears 527 times in the training set and “Bad Credit” (0) 223, two times less. Since there are many more “Good Credit” than “Bad Credit”, any model favors the prediction of the “Good Credit”. It results a good accuracy but the specificity is low, as well as the balanced accuracy.
Sub-sampling
Balancing using sub-sampling consists of taking all the cases in the smallest class (here “Bad Credit”) and extract at random the same amount of cases in the largest category (here “Good”).
The training set is now balanced, we have 223
observations for both “Good Credit” (1) and “Bad Credit” (0). The new
balanced training set is called German_Credit.tr.subs.
Models Fitting
Once we had our training set and test set, we could fit some models and compare them with together to choose the best model.
1. Classification Tree (Decision Tree)
We first started with a decision tree and more specifically we chose
the classification tree as we want to classify the applicants. The model
was build on our previously balanced training set
German_Credit.tr.subs. We used the R function
rpart.
We obtained the following large tree.
We could see that among the 31 explanatory variables, this model uses 6 of them: CHK_ACCT, AMOUNT, HISTORY, DURATION, GUARANTOR and EMPLOYMENT.
| Bad credit risk | Good credit risk | |
|---|---|---|
| Bad credit risk | 58 | 70 |
| Good credit risk | 19 | 103 |
## Sensitivity Specificity Pos Pred Value
## 0.7532468 0.5953757 0.4531250
## Neg Pred Value Precision Recall
## 0.8442623 0.4531250 0.7532468
## F1 Prevalence Detection Rate
## 0.5658537 0.3080000 0.2320000
## Detection Prevalence Balanced Accuracy
## 0.5120000 0.6743112We first have an insight on how well it predict the test set
(German_credit.te ). We recall that 0 means a “Bad Credit”
risk and 1 means a “Good Credit” risk. It seems that this model has
difficulty to predict the “Bad Credit” risk applicants. Indeed from the
table have 70 observations that were misclassified as being “Bad credit”
while it was in fact a “Good credit”.
As the tree is quite big and we want to know if we can prune it. To
do so, we decided to use the printcp and
plotcp commands and choose the best cp
(complexity parameter) value to prune our tree.
Pruning the tree
##
## Classification tree:
## rpart(formula = RESPONSE ~ ., data = German_Credit.tr.subs, method = "class")
##
## Variables actually used in tree construction:
## [1] AMOUNT CHK_ACCT DURATION EMPLOYMENT GUARANTOR HISTORY
##
## Root node error: 223/446 = 0.5
##
## n= 446
##
## CP nsplit rel error xerror xstd
## 1 0.399103 0 1.00000 1.08520 0.047179
## 2 0.022422 1 0.60090 0.63677 0.044117
## 3 0.014574 2 0.57848 0.66816 0.044668
## 4 0.011958 7 0.48430 0.69058 0.045028
## 5 0.011211 10 0.44843 0.67265 0.044742
## 6 0.010000 12 0.42601 0.67265 0.044742
From the list of cp (complexity parameter), we would choose the line that has the lowest cross validation error. This can be seen on the column xerror. So the best cp would be 0.022422 with one split.
From the graph, we can identify that, according to the 1-SE rule, the tree with 2 and 3 are equivalent. The tree with 3 nodes should be preferred. It appears below the dotted-line.
The value of cp can be chosen arbitrarily between 0.018 and 0.095. So we decided to go with the suggested cp of 0.022 from the summary.
With these value, we obtain a very small tree.
This pruned decision tree with a cp of 0.022 uses the variables CHK_ACCT and HISTORY.
Using this pruned tree, we can computed the prediction and build a confusion matrix to see the performance of the model.
| Bad credit risk | Good credit risk | |
|---|---|---|
| Bad credit risk | 63 | 95 |
| Good credit risk | 14 | 78 |
## Sensitivity Specificity Pos Pred Value
## 0.8181818 0.4508671 0.3987342
## Neg Pred Value Precision Recall
## 0.8478261 0.3987342 0.8181818
## F1 Prevalence Detection Rate
## 0.5361702 0.3080000 0.2520000
## Detection Prevalence Balanced Accuracy
## 0.6320000 0.6345244Here again, this model has difficulty to predict the “Bad credit” cases. The model also decreased in its precision values.
We also decided to look at what would an automatically pruned using 1-SE rule would give us and whether or not it is better than the pruned tree we made by looking at the cp.
Here, only the variable CHK_ACCT is used. As we prune the tree more information are lost.
| Bad credit risk | Good credit risk | |
|---|---|---|
| Bad credit risk | 61 | 88 |
| Good credit risk | 16 | 85 |
## Sensitivity Specificity Pos Pred Value
## 0.7922078 0.4913295 0.4093960
## Neg Pred Value Precision Recall
## 0.8415842 0.4093960 0.7922078
## F1 Prevalence Detection Rate
## 0.5398230 0.3080000 0.2440000
## Detection Prevalence Balanced Accuracy
## 0.5960000 0.6417686Again, it seems that in general the classification trees we perfomed have difficulty to predict the “Bad credit” cases.
Variable importance of the classification tree
Then we analysed the variable importance of one of the models. We
decided to compute the variable importance of the pruned
classisication tree german.ct.prune by applying
the function varImp on the model.
It is summarized below on the plot.
From this plot, we see that the variables that influences the most are CHK_ACCT, HISTORY, SAV_ACCT, DURATION, AMOUNT and REAL_ESTATE. They are not exactly the same as the one we saw above.
The variable CHK_ACCT and HISTORY were already noticed though.
2. Logistic Regression
The next model we performed is a logistic regression.
##
## Call:
## glm(formula = RESPONSE ~ ., family = binomial, data = German_Credit.tr.subs)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.34578 -0.68043 0.00049 0.65178 2.74937
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.1911402 1.7958756 0.663 0.507161
## CHK_ACCT1 0.5692882 0.3363406 1.693 0.090533 .
## CHK_ACCT2 0.8404451 0.5339512 1.574 0.115485
## CHK_ACCT3 2.4337691 0.3770606 6.455 1.09e-10 ***
## DURATION -0.0123731 0.0142153 -0.870 0.384078
## HISTORY1 -1.0734853 0.8514386 -1.261 0.207384
## HISTORY2 0.0865599 0.6747882 0.128 0.897930
## HISTORY3 -0.0598560 0.7410028 -0.081 0.935619
## HISTORY4 1.1072483 0.6576414 1.684 0.092246 .
## NEW_CAR1 -0.4538649 0.5853211 -0.775 0.438096
## USED_CAR1 1.6322817 0.7540134 2.165 0.030404 *
## FURNITURE1 0.0509645 0.6182782 0.082 0.934305
## RADIO.TV1 0.5261147 0.5896893 0.892 0.372291
## EDUCATION1 0.5441469 0.7499724 0.726 0.468111
## RETRAINING1 -0.4293160 0.6787931 -0.632 0.527080
## AMOUNT -0.0002155 0.0000739 -2.916 0.003550 **
## SAV_ACCT1 0.6181742 0.4475399 1.381 0.167195
## SAV_ACCT2 -0.2531524 0.5541205 -0.457 0.647776
## SAV_ACCT3 0.7292579 0.6813687 1.070 0.284492
## SAV_ACCT4 1.4221687 0.4243610 3.351 0.000804 ***
## EMPLOYMENT1 0.7574673 0.7956778 0.952 0.341108
## EMPLOYMENT2 1.4785839 0.7640267 1.935 0.052959 .
## EMPLOYMENT3 1.9691166 0.7947873 2.478 0.013229 *
## EMPLOYMENT4 1.8560330 0.7511387 2.471 0.013475 *
## INSTALL_RATE -0.3367533 0.1411404 -2.386 0.017035 *
## MALE_DIV1 -0.5653453 0.5705857 -0.991 0.321775
## MALE_SINGLE1 0.1618525 0.3327207 0.486 0.626647
## MALE_MAR_or_WID1 -0.5551862 0.5312986 -1.045 0.296041
## CO.APPLICANT1 -0.6994379 0.6920599 -1.011 0.312179
## GUARANTOR1 1.7126786 0.6556150 2.612 0.008993 **
## PRESENT_RESIDENT2 -1.1195205 0.4773294 -2.345 0.019008 *
## PRESENT_RESIDENT3 -0.2590309 0.5313455 -0.487 0.625904
## PRESENT_RESIDENT4 -0.9082582 0.4793144 -1.895 0.058104 .
## REAL_ESTATE1 -0.0137202 0.3384983 -0.041 0.967669
## PROP_UNKN_NONE1 -1.4578770 0.6505748 -2.241 0.025032 *
## AGE 0.0167050 0.0141041 1.184 0.236255
## OTHER_INSTALL1 -0.6758552 0.3404321 -1.985 0.047113 *
## RENT1 -1.2066453 0.8244600 -1.464 0.143315
## OWN_RES1 -0.4707135 0.7665544 -0.614 0.539173
## NUM_CREDITS -0.3634820 0.3011721 -1.207 0.227474
## JOB1 -0.7402802 1.1619781 -0.637 0.524069
## JOB2 -1.2142377 1.1317833 -1.073 0.283337
## JOB3 -1.4358446 1.1604352 -1.237 0.215964
## NUM_DEPENDENTS 0.1270172 0.3832474 0.331 0.740325
## TELEPHONE1 0.6259633 0.3143236 1.991 0.046430 *
## FOREIGN1 1.2496315 0.8543880 1.463 0.143576
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 618.29 on 445 degrees of freedom
## Residual deviance: 390.97 on 400 degrees of freedom
## AIC: 482.97
##
## Number of Fisher Scoring iterations: 5We see that a lot of variables are not statistically significant for the model so we can think of a model reduction.
Before doing a reduction of the model, we fitted the model and predicted on the test set.
| Bad credit risk | Good credit risk | |
|---|---|---|
| Bad credit risk | 49 | 46 |
| Good credit risk | 28 | 127 |
## Sensitivity Specificity Pos Pred Value
## 0.6363636 0.7341040 0.5157895
## Neg Pred Value Precision Recall
## 0.8193548 0.5157895 0.6363636
## F1 Prevalence Detection Rate
## 0.5697674 0.3080000 0.1960000
## Detection Prevalence Balanced Accuracy
## 0.3800000 0.6852338From the confusion matrix, we see again the the model has difficulty to predict the “Bad credit” althought the wronged classified amount of observation is lower when it comes to the “Bad credit” one.
Variable selection and interpretation with step method (AIC criteria)
In order to reduce the logistic regression we used a stepwise
variable selection. This has been done with the command
step.
The final reduced model is as follow.
##
## Call:
## glm(formula = RESPONSE ~ CHK_ACCT + HISTORY + NEW_CAR + USED_CAR +
## RETRAINING + AMOUNT + SAV_ACCT + EMPLOYMENT + INSTALL_RATE +
## GUARANTOR + PRESENT_RESIDENT + PROP_UNKN_NONE + AGE + OTHER_INSTALL +
## RENT + TELEPHONE + FOREIGN, family = binomial, data = German_Credit.tr.subs)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.39343 -0.68768 -0.02628 0.71315 2.60726
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.6339113 1.1570626 -0.548 0.583786
## CHK_ACCT1 0.5970566 0.3291383 1.814 0.069678 .
## CHK_ACCT2 1.1123874 0.5042812 2.206 0.027392 *
## CHK_ACCT3 2.4109175 0.3597629 6.701 2.06e-11 ***
## HISTORY1 -0.6393459 0.8007632 -0.798 0.424626
## HISTORY2 0.3153810 0.6295178 0.501 0.616379
## HISTORY3 0.0245812 0.7411154 0.033 0.973541
## HISTORY4 1.0638624 0.6476870 1.643 0.100475
## NEW_CAR1 -0.7159178 0.3141611 -2.279 0.022678 *
## USED_CAR1 1.3489217 0.5579072 2.418 0.015614 *
## RETRAINING1 -0.8489518 0.4619050 -1.838 0.066072 .
## AMOUNT -0.0002631 0.0000595 -4.421 9.81e-06 ***
## SAV_ACCT1 0.5675624 0.4173990 1.360 0.173906
## SAV_ACCT2 -0.0693577 0.5399345 -0.128 0.897788
## SAV_ACCT3 0.5603771 0.6437202 0.871 0.384011
## SAV_ACCT4 1.3592948 0.4069584 3.340 0.000837 ***
## EMPLOYMENT1 0.5542570 0.6967423 0.795 0.426324
## EMPLOYMENT2 1.2338686 0.6524020 1.891 0.058588 .
## EMPLOYMENT3 1.7999683 0.6887566 2.613 0.008966 **
## EMPLOYMENT4 1.5521376 0.6518729 2.381 0.017264 *
## INSTALL_RATE -0.3278020 0.1249721 -2.623 0.008716 **
## GUARANTOR1 1.6927223 0.6068573 2.789 0.005282 **
## PRESENT_RESIDENT2 -1.1117822 0.4641005 -2.396 0.016595 *
## PRESENT_RESIDENT3 -0.3408387 0.5041109 -0.676 0.498966
## PRESENT_RESIDENT4 -0.7613632 0.4531619 -1.680 0.092935 .
## PROP_UNKN_NONE1 -1.0532655 0.3848454 -2.737 0.006203 **
## AGE 0.0181856 0.0128738 1.413 0.157769
## OTHER_INSTALL1 -0.6281982 0.3256821 -1.929 0.053747 .
## RENT1 -0.8736712 0.3412119 -2.560 0.010452 *
## TELEPHONE1 0.5251823 0.2863172 1.834 0.066614 .
## FOREIGN1 1.2896516 0.8049248 1.602 0.109111
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 618.29 on 445 degrees of freedom
## Residual deviance: 403.37 on 415 degrees of freedom
## AIC: 465.37
##
## Number of Fisher Scoring iterations: 5The variables that have been removed are : FURNITURE, RADIO.TV, EDUCATION, RETRAINING, MALE_DIV, MALE_SINGLE, MALE_MAR_or_WID, CO.APPLICANT, REAL_ESTATE, OWN_RES, NUM_CREDITS, JOB and NUM_DEPENDENTS
In the end, we get the most significant model:
\[ RESPONSE = -0.6339113 + 0.5970566 * CHK_{ACCT1} + 1.1123874 * CHK_{ACCT2} + 2.4109175 * CHK_{ACCT3} - 0.6393459 * HISTORY1 + 0.3153810 * HISTORY2 \\ + 0.0245812 * HISTORY3 + 1.0638624 * HISTORY4 - 0.7159178 * NEW_{CAR1} \\ + 1.3489217 * USED_{CAR1} -0.8489518 * RETRAINING1 - 0.0002631 * AMOUNT \\ + 0.5675624 * SAV_{ACCT1} - 0.0693577 * SAV_{ACCT2} + 0.5603771 * SAV_{ACCT3} \\ + 1.3592948 * * SAV_{ACCT4} + 0.5542570 * EMPLOYMENT1 + 1.2338686 * EMPLOYMENT2 \\ + 1.7999683 * EMPLOYMENT3 + 1.5521376 * EMPLOYMENT4 - 0.3278020 * INSTALL_{RATE} \\ + 1.6927223 * GUARANTOR1 - 1.1117822 * PRESENT_{RESIDENT2} \\ - 0.3408387 * PRESENT_{RESIDENT3} - 0.7613632 * PRESENT_{RESIDENT4} \\ - 1.0532655 * PROP_{UNKN_NONE1} + 0.0181856 * AGE - 0.6281982 * OTHER_{INSTALL1} \\ - 0.8736712 * RENT1 + 0.5251823 * TELEPHONE + 1.2896516 * FOREIGN \]
\[ p = (e^{RESPONSE})/(1 + e^{RESPONSE})\]
It means that :
- The predicted probability of being a good applicant for CHCK_ACCT3 is higher than for CHK_ACCT0 (and also higher than for CHK_ACCT1 and CHK_ACCT2).
- The predicted probability of being a good applicant for HISTORY1 is lower than for HISTORY0.
- The predicted probability of being a good applicant for HISTORY4 is higher than for HISTORY0 (and also higher than for HISTORY2 and HISTORY3).
- The predicted probability of being a good applicant for NEW_CAR1 is lower than for NEW_CAR0.
- The predicted probability of being a good applicant for USED_CAR1 is higher than for USED_CAR0.
- The predicted probability of being a good applicant for RETRAINING1 is lower than for RETRAINING0.
- AMOUNT is negatively associated with RESPONSE.
- The predicted probability of being a good applicant for SAV_ACCT4 is higher than for SAV_ACCT0 (and also higher than for SAV_ACCT1 and SAV_ACCT3).
- The predicted probability of being a good applicant for SAV_ACCT2 lower than for SAV_ACCT0.
- The predicted probability of being a good applicant for EMPLOYMENT3 is higher than for Employment0 (and also higher than for EMPLOYMENT1, EMPLOYMENT2 and EMPLOYMENT4).
- INSTALL_RATE is negatively associated with RESPONSE.
- The predicted probability of being a good applicant for GUARANTOR1 is higher than for GUARANTOR0.
- The predicted probability of being a good applicant for PRESENT_RESIDENT2 is lower than for PRESENT_RESIDENT0 (and also lower than PRESENT_RESIDENT3 and PRESENT_RESIDENT4).
- The predicted probability of being a good applicant for PROP_UNKN_NONE1 is lower than for PROP_UNKN_NONE0.
- AGE is positively associated with RESPONSE.
- The predicted probability of being a good applicant for OTHER_INSTALL1 is lower than for OTHER_INSTALL0.
- The predicted probability of being a good applicant for RENT1 is lower than for RENT0.
- The predicted probability of being a good applicant for TELEPHONE1 is higher than for TELEPHONE0.
- The predicted probability of being a good applicant for FOREIGN1 is higher than for FOREIGN0.
| Bad credit risk | Good credit risk | |
|---|---|---|
| Bad credit risk | 50 | 52 |
| Good credit risk | 27 | 121 |
## Sensitivity Specificity Pos Pred Value
## 0.6493506 0.6994220 0.4901961
## Neg Pred Value Precision Recall
## 0.8175676 0.4901961 0.6493506
## F1 Prevalence Detection Rate
## 0.5586592 0.3080000 0.2000000
## Detection Prevalence Balanced Accuracy
## 0.4080000 0.6743863From this point we might think that the problem for the difficulty to predict the “Bad Credit” cases is not due to the models but rather the data itself. We might still want to perfom other models to make sure of our intuition.
Variable importance for logistic regression
Listed above are the most important variables for the logarithmic regression we reduced. Here again, the CHK_ACCT variable differentiate itself from the others in term of importance in the model prediction.
3.a K-Nearest Neighbor (K=2)
To perform a k-nearest neighbor method, we do not need to balance the data so we will use the unbalanced training set.
We first try to model it using a 2-NN (with Euclidean distance). Note that the model is fitting on the training set and the predictions are computed on the test set.
| Bad credit risk | Good credit risk | |
|---|---|---|
| Bad credit risk | 21 | 45 |
| Good credit risk | 56 | 128 |
## Sensitivity Specificity Pos Pred Value
## 0.2727273 0.7398844 0.3181818
## Neg Pred Value Precision Recall
## 0.6956522 0.3181818 0.2727273
## F1 Prevalence Detection Rate
## 0.2937063 0.3080000 0.0840000
## Detection Prevalence Balanced Accuracy
## 0.2640000 0.5063058The table is read as follow :
- We predicted 21 Bad credits and there were indeed 21 observed Bad credits. But the prediction misjudges 45 good credits by predicting them as bad credits.
- We predicted 128 Good credits as it was in fact a Good credits but 56 where predicted as Good while it was in fact Bad.
So again, this model also have difficulties to predict the “Bad Credit” cases.
The prediction is not perfect. We need to try to improve the prediction by changing K at that point. Therefore, we use K=3.
3.b K-Nearest Neighbor (K=3)
| Bad credit risk | Good credit risk | |
|---|---|---|
| Bad credit risk | 58 | 70 |
| Good credit risk | 19 | 103 |
## Sensitivity Specificity Pos Pred Value
## 0.1818182 0.8381503 0.3333333
## Neg Pred Value Precision Recall
## 0.6971154 0.3333333 0.1818182
## F1 Prevalence Detection Rate
## 0.2352941 0.3080000 0.0560000
## Detection Prevalence Balanced Accuracy
## 0.1680000 0.5099842The table is read as follow :
- We predicted 58 Bad credits and they were indeed observed Bad credits. But the prediction misjudges 70 good credits by predicting them as being bad credits.
- We predicted 103 Good credits as it was in fact a Good credits but 19 where predicted as Good while it was in fact Bad.
Again it seems not to have improved anything, the F-measure even seems to have decreased a little bit.
4. Linear Support Vector Machine
The next model is the linear Support Vector Machine.
##
## Call:
## svm(formula = RESPONSE ~ ., data = German_Credit.tr.subs, kernel = "linear")
##
##
## Parameters:
## SVM-Type: C-classification
## SVM-Kernel: linear
## cost: 1
##
## Number of Support Vectors: 246| Bad credit risk | Good credit risk | |
|---|---|---|
| Bad credit risk | 50 | 50 |
| Good credit risk | 27 | 123 |
## Sensitivity Specificity Pos Pred Value
## 0.6493506 0.7109827 0.5000000
## Neg Pred Value Precision Recall
## 0.8200000 0.5000000 0.6493506
## F1 Prevalence Detection Rate
## 0.5649718 0.3080000 0.2000000
## Detection Prevalence Balanced Accuracy
## 0.4000000 0.6801667This model seems to have improved a little bit our ability to predict the “Bad Credit” cases. As half of the “Bad Credit” predicted by the model are correct.
Tunning the hyperparameters of Linear SVM
We want to select the good hyperparameters for our linear SVM.
## Support Vector Machines with Linear Kernel
##
## 446 samples
## 30 predictor
## 2 classes: '0', '1'
##
## No pre-processing
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 402, 400, 402, 401, 402, 402, ...
## Resampling results:
##
## Accuracy Kappa
## 0.7264361 0.4530209
##
## Tuning parameter 'C' was held constant at a value of 1We see that we have a good accuracy (0.72).
## Support Vector Machines with Linear Kernel
##
## 446 samples
## 30 predictor
## 2 classes: '0', '1'
##
## No pre-processing
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 402, 400, 402, 401, 402, 402, ...
## Resampling results across tuning parameters:
##
## C Accuracy Kappa
## 1e-02 0.7264339 0.4532044
## 1e-01 0.7286056 0.4575791
## 1e+00 0.7264361 0.4530209
## 1e+01 0.7108278 0.4216992
## 1e+02 0.7130501 0.4261940
## 1e+03 0.7197672 0.4397558
##
## Accuracy was used to select the optimal model using the largest value.
## The final value used for the model was C = 0.1.
| Bad credit risk | Good credit risk | |
|---|---|---|
| Bad credit risk | 49 | 49 |
| Good credit risk | 28 | 124 |
## Sensitivity Specificity Pos Pred Value
## 0.6363636 0.7167630 0.5000000
## Neg Pred Value Precision Recall
## 0.8157895 0.5000000 0.6363636
## F1 Prevalence Detection Rate
## 0.5600000 0.3080000 0.1960000
## Detection Prevalence Balanced Accuracy
## 0.3920000 0.6765633Again, half of the “Bad Credit” predicted observations are indeed “Bad credit”.
The Linear support vector models are not too bad in the sense that they are better that the models we have seen so far.
5. Radial Basis Support Vector Machine
We try now with a radial basis kernel (the default).
##
## Call:
## svm(formula = RESPONSE ~ ., data = German_Credit.tr.subs, kernel = "radial")
##
##
## Parameters:
## SVM-Type: C-classification
## SVM-Kernel: radial
## cost: 1
##
## Number of Support Vectors: 334| Bad credit risk | Good credit risk | |
|---|---|---|
| Bad credit risk | 54 | 52 |
| Good credit risk | 23 | 121 |
## Sensitivity Specificity Pos Pred Value
## 0.7012987 0.6994220 0.5094340
## Neg Pred Value Precision Recall
## 0.8402778 0.5094340 0.7012987
## F1 Prevalence Detection Rate
## 0.5901639 0.3080000 0.2160000
## Detection Prevalence Balanced Accuracy
## 0.4240000 0.7003603This model performance is very close to the linear support vector models. We need to infer more by looking at the tunned version.
Tunning the hyperparameters of Radial basis SVM
## Support Vector Machines with Radial Basis Function Kernel
##
## 446 samples
## 30 predictor
## 2 classes: '0', '1'
##
## No pre-processing
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 402, 400, 402, 401, 402, 402, ...
## Resampling results across tuning parameters:
##
## sigma C Accuracy Kappa
## 0.01 1 0.7309289 0.4618150
## 0.01 10 0.6971476 0.3942416
## 0.01 100 0.6907708 0.3814209
## 0.01 500 0.6975889 0.3950572
## 0.01 1000 0.6975889 0.3950572
## 0.02 1 0.7309816 0.4620420
## 0.02 10 0.6972925 0.3946754
## 0.02 100 0.7064273 0.4127482
## 0.02 500 0.7064273 0.4127482
## 0.02 1000 0.7064273 0.4127482
## 0.05 1 0.7038647 0.4085756
## 0.05 10 0.6860299 0.3726705
## 0.05 100 0.6860299 0.3726705
## 0.05 500 0.6860299 0.3726705
## 0.05 1000 0.6860299 0.3726705
## 0.10 1 0.6588603 0.3190546
## 0.10 10 0.6611792 0.3234506
## 0.10 100 0.6611792 0.3234506
## 0.10 500 0.6611792 0.3234506
## 0.10 1000 0.6611792 0.3234506
##
## Accuracy was used to select the optimal model using the largest value.
## The final values used for the model were sigma = 0.02 and C = 1.
## sigma C
## 6 0.02 1| Bad credit risk | Good credit risk | |
|---|---|---|
| Bad credit risk | 54 | 53 |
| Good credit risk | 23 | 120 |
## Sensitivity Specificity Pos Pred Value
## 0.7012987 0.6936416 0.5046729
## Neg Pred Value Precision Recall
## 0.8391608 0.5046729 0.7012987
## F1 Prevalence Detection Rate
## 0.5869565 0.3080000 0.2160000
## Detection Prevalence Balanced Accuracy
## 0.4280000 0.6974702The model seems to be well balanced and it has good scores. The F-measure is quite high as well.
6. Neural Network - Simple hyperparameter tuning
To select the good parameters, we build a search grid and fit the model with each possible value in the grid. This is brute force and time consuming. The best model is selected among all the possible choices.
The best Neural Networks parameters would be to choose 3 hidden layers,
with a decay of 0.4.
| Bad credit risk | Good credit risk | |
|---|---|---|
| Bad credit risk | 52 | 53 |
| Good credit risk | 25 | 120 |
## Sensitivity Specificity Pos Pred Value
## 0.6753247 0.6936416 0.4952381
## Neg Pred Value Precision Recall
## 0.8275862 0.4952381 0.6753247
## F1 Prevalence Detection Rate
## 0.5714286 0.3080000 0.2080000
## Detection Prevalence Balanced Accuracy
## 0.4200000 0.6844831We see that this Neural Network competes quite close to the support vector machines ones. Almost half of the “Bad credit” cases that it has predicted are correct.
7. Gradient Boosting
The Gradient Boosting model accepts only numerical values so we have some transformation to do on our data in order to use it.
## ##### xgb.Booster
## raw: 31.2 Mb
## call:
## xgb.train(params = xgb_params, data = xgb_train, nrounds = 5000,
## verbose = 1)
## params (as set within xgb.train):
## booster = "gbtree", eta = "0.01", max_depth = "8", gamma = "4", subsample = "0.75", colsample_bytree = "1", objective = "multi:softmax", eval_metric = "mlogloss", num_class = "2", validate_parameters = "TRUE"
## xgb.attributes:
## niter
## callbacks:
## cb.print.evaluation(period = print_every_n)
## # of features: 46
## niter: 5000
## nfeatures : 46Here we have an accuracy of 68.4%. It is good but there is room for improvement.
| Bad credit risk | Good credit risk | |
|---|---|---|
| Bad credit risk | 57 | 59 |
| Good credit risk | 20 | 114 |
## Sensitivity Specificity Pos Pred Value
## 0.7402597 0.6589595 0.4913793
## Neg Pred Value Precision Recall
## 0.8507463 0.4913793 0.7402597
## F1 Prevalence Detection Rate
## 0.5906736 0.3080000 0.2280000
## Detection Prevalence Balanced Accuracy
## 0.4640000 0.6996096Review of statistics
Once all the models were modelized we compared them according to their scores and metrics. Below we summarized all their accuracy into one table.
| Big classification tree | Pruned classification tree | Autoprune classification tree | Logistic regression | AIC reduced Logistic regression | Linear support vector machine | |
|---|---|---|---|---|---|---|
| Accuracy | 0.644 | 0.564 | 0.584 | 0.704 | 0.684 | 0.692 |
| Kappa | 0.2945 | 0.2083 | 0.2251 | 0.3479 | 0.32 | 0.3328 |
| Accuracy lower bound | 0.5812 | 0.5001 | 0.5202 | 0.6432 | 0.6224 | 0.6307 |
| Accuracy upper bound | 0.7033 | 0.6264 | 0.6458 | 0.7599 | 0.7411 | 0.7486 |
| Accuracy null | 0.692 | 0.692 | 0.692 | 0.692 | 0.692 | 0.692 |
| Accuracy P-value | 0.9552 | 1 | 0.9999 | 0.369 | 0.6369 | 0.5308 |
| Mcnemar P-value | 1.158e-07 | 1.822e-14 | 3.352e-12 | 0.04813 | 0.00693 | 0.01217 |
| Tuned linear support vector machine | Radial base support vector machine | Tuned radial base support vector machine | Hyperparameter tuned neural network 3 nodes | Gradient Boosting | |
|---|---|---|---|---|---|
| Accuracy | 0.692 | 0.7 | 0.696 | 0.688 | 0.684 |
| Kappa | 0.3283 | 0.3628 | 0.3564 | 0.3352 | 0.35 |
| Accuracy lower bound | 0.6307 | 0.6391 | 0.6349 | 0.6266 | 0.6224 |
| Accuracy upper bound | 0.7486 | 0.7561 | 0.7524 | 0.7449 | 0.7411 |
| Accuracy null | 0.692 | 0.692 | 0.692 | 0.692 | 0.692 |
| Accuracy P-value | 0.5308 | 0.4219 | 0.4762 | 0.5847 | 0.6369 |
| Mcnemar P-value | 0.02265 | 0.001224 | 0.0008794 | 0.002235 | 1.909e-05 |
According to these two first tables, the best model would be the “Radial base linear support vector machine” as it has the highest accuracy level of 0.7 and the best kappa value of 0.3628.
The accuracy means that out of total number of observations, the model predicted correctly 70% of them. The Cohen’s Kappa Coefficient means that there is 36% of agreement, indicating that the raters agree in their classification for 36% of the cases.
We also remember that the model was almost better than the other models when it came to predict the “Bad credit” cases. Although the model remains quite poor at predicting them since only half of the predicted ones are correct.
Another table is done to compare the KNN because they were not performed on the balanced dataset.
| 2-Nearest neighbor | 3-Nearest neighbor | |
|---|---|---|
| Accuracy | 0.596 | 0.636 |
| Kappa | 0.01313 | 0.02285 |
| AccuracyLower | 0.5323 | 0.573 |
| AccuracyUpper | 0.6574 | 0.6957 |
| AccuracyNull | 0.692 | 0.692 |
| AccuracyPValue | 0.9995 | 0.9752 |
| McnemarPValue | 0.3197 | 0.000365 |
Overall, we see that the worst model is the ‘Autoprune classification tree’. This is understandable because we pruned the model so much that we lost many observations on the way.
Conclusion
Recall, we computed several models. We first started with three versions of the classification tree, then we performed two logistic regression, two neares neighbour, four support vector machines, one neural network and one gradient boosting model. Through all these models we noticed a common point which was their poor ability to predict the “Bad credit” cases. Knowing the purpose of this report, it is not really good as the banker might then misjudge the new applicant and refuse to give a credit while the applicant might be a good one. This will result in an opportunity loss for our client, the banker.
Since several models has been performed throughout this analysis, we came up with the conclusion that there might be a bias in the data itself. Indeed we might have good information and knowledge on the characteristics of a “good” applicant but the data could be improved and include more information on the “bad” applicant. This way, the models will then be able to be better trained.
Our recommendations/Suggestions
As we saw the models could be improved as the accuracies are not going over the 70%. We think that others variables describing better the ‘Bad’ credits could be added. For example, it would be interesting to know whether the applicant is under litigation for not paying back someone (‘acte de poursuite’ in French).
References
Annexes
Appendix A : Definitions of the attributes of the German Credit dataset
- OBS# : Observation No.
- CHK_ACCT : Checking account status
- 0 : < 0 DM
- 1 : 0 < · · · < 200 DM
- 2 : ≥ 200 DM
- 3 : no checking account
- DURATION : Duration of credit in months
- HISTORY : Credit history
- 0 : no credits taken
- 1 : all credits at this bank paid back duly
- 2 : existing credits paid back duly till now
- 3 : delay in paying off in the past
- 4 : critical account
- NEW_CAR : Purpose of credit
- car (new) 0 : No, 1 : Yes
- USED_CAR : Purpose of credit
- car (used) 0 : No, 1 : Yes
- FURNITURE : Purpose of credit
- furniture/equipment 0 : No, 1 : Yes
- RADIO/TV : Purpose of credit
- radio/television 0 : No, 1 : Yes
- EDUCATION Purpose of credit
- education 0 : No, 1 : Yes
- RETRAINING Purpose of credit
- retraining 0 : No, 1 : Yes
- AMOUNT : Credit amount
- SAV_ACCT : Average balance in savings account
- 0 : < 100 DM
- 1 : 100 ≤ · · · < 500 DM
- 2 : 500 ≤ · · · < 1000 DM
- 3 : ≥ 1000 DM
- 4 : unknown/no savings account
- EMPLOYMENT : Present employment since
- 0 : unemployed
- 1 : < 1 year
- 2 : 1 ≤ · · · < 4 years
- 3 : 4 ≤ · · · < 7 years
- 4 : ≥ 7 years
- INSTALL_RATE : Installment rate as % of disposable income
- MALE_DIV : Applicant is male and divorced
- 0 : No, 1 : Yes
- MALE_SINGLE : Applicant is male and single
- 0 : No, 1 : Yes
- MALE_MAR_WID : Applicant is male and married or a widower
- 0 : No, 1 : Yes
- CO−APPLICANT : Application has a co-applicant
- 0 : No, 1 : Yes
- GUARANTOR : Applicant has a guarantor
- 0 : No, 1 : Yes
- PRESENT_RESIDENT : Present resident since - years
- 0 : ≤ 1 year
- 1 : 1 < · · · ≤ 2 years
- 2 : 2 < · · · ≤ 3 years
- 3 :> 4 years
- REAL_ESTATE : Applicant owns real estate
- 0 : No, 1 : Yes
- PROP_UNKN_NONE : Applicant owns no property (or unknown)
- 0 : No, 1 : Yes
- AGE : Age in years
- OTHER_INSTALL : Applicant has other installment plan credit
- 0 : No, 1 : Yes
- RENT : Applicant rents
- 0 : No, 1 : Yes
- OWN_RES : Applicant owns residence
- 0 : No, 1 : Yes
- NUM_CREDITS : Number of existing credits at this bank
- JOB : Nature of job
- 0 : unemployed/unskilled non-resident
- 1 : unskilled - resident
- 2 : skilled employee/official
- 3 : management/self-employed/
- highly qualified employee/officer
- NUM_DEPENDENTS : Number of people for whom liable to provide maintenance
- TELEPHONE : Applicant has phone in his or her name
- 0 : No, 1 : Yes
- FOREIGN + Foreign worker
- 0 : No, 1 : Yes
Appendix B : Barplots of the categorical variables from the EDA part.
Appendix C : General summary of the German Credit dataset
## Data Frame Summary
## Dimensions: 1000 x 32
## Duplicates: 0
##
## +----+------------------+-----------------------------+---------------------+-----------------------+----------+---------+
## | No | Variable | Stats / Values | Freqs (% of Valid) | Graph | Valid | Missing |
## +====+==================+=============================+=====================+=======================+==========+=========+
## | 1 | OBS. | 1. 1 | 1 ( 0.1%) | | 1000 | 0 |
## | | [factor] | 2. 2 | 1 ( 0.1%) | | (100.0%) | (0.0%) |
## | | | 3. 3 | 1 ( 0.1%) | | | |
## | | | 4. 4 | 1 ( 0.1%) | | | |
## | | | 5. 5 | 1 ( 0.1%) | | | |
## | | | 6. 6 | 1 ( 0.1%) | | | |
## | | | 7. 7 | 1 ( 0.1%) | | | |
## | | | 8. 8 | 1 ( 0.1%) | | | |
## | | | 9. 9 | 1 ( 0.1%) | | | |
## | | | 10. 10 | 1 ( 0.1%) | | | |
## | | | [ 990 others ] | 990 (99.0%) | IIIIIIIIIIIIIIIIIII | | |
## +----+------------------+-----------------------------+---------------------+-----------------------+----------+---------+
## | 2 | CHK_ACCT | 1. 0 | 274 (27.4%) | IIIII | 1000 | 0 |
## | | [factor] | 2. 1 | 269 (26.9%) | IIIII | (100.0%) | (0.0%) |
## | | | 3. 2 | 63 ( 6.3%) | I | | |
## | | | 4. 3 | 394 (39.4%) | IIIIIII | | |
## +----+------------------+-----------------------------+---------------------+-----------------------+----------+---------+
## | 3 | DURATION | Mean (sd) : 20.9 (12.1) | 33 distinct values | : | 1000 | 0 |
## | | [numeric] | min < med < max: | | : : | (100.0%) | (0.0%) |
## | | | 4 < 18 < 72 | | . : : | | |
## | | | IQR (CV) : 12 (0.6) | | : : : . | | |
## | | | | | : : : : : . : | | |
## +----+------------------+-----------------------------+---------------------+-----------------------+----------+---------+
## | 4 | HISTORY | 1. 0 | 40 ( 4.0%) | | 1000 | 0 |
## | | [factor] | 2. 1 | 49 ( 4.9%) | | (100.0%) | (0.0%) |
## | | | 3. 2 | 530 (53.0%) | IIIIIIIIII | | |
## | | | 4. 3 | 88 ( 8.8%) | I | | |
## | | | 5. 4 | 293 (29.3%) | IIIII | | |
## +----+------------------+-----------------------------+---------------------+-----------------------+----------+---------+
## | 5 | NEW_CAR | 1. 0 | 766 (76.6%) | IIIIIIIIIIIIIII | 1000 | 0 |
## | | [factor] | 2. 1 | 234 (23.4%) | IIII | (100.0%) | (0.0%) |
## +----+------------------+-----------------------------+---------------------+-----------------------+----------+---------+
## | 6 | USED_CAR | 1. 0 | 897 (89.7%) | IIIIIIIIIIIIIIIII | 1000 | 0 |
## | | [factor] | 2. 1 | 103 (10.3%) | II | (100.0%) | (0.0%) |
## +----+------------------+-----------------------------+---------------------+-----------------------+----------+---------+
## | 7 | FURNITURE | 1. 0 | 819 (81.9%) | IIIIIIIIIIIIIIII | 1000 | 0 |
## | | [factor] | 2. 1 | 181 (18.1%) | III | (100.0%) | (0.0%) |
## +----+------------------+-----------------------------+---------------------+-----------------------+----------+---------+
## | 8 | RADIO.TV | 1. 0 | 720 (72.0%) | IIIIIIIIIIIIII | 1000 | 0 |
## | | [factor] | 2. 1 | 280 (28.0%) | IIIII | (100.0%) | (0.0%) |
## +----+------------------+-----------------------------+---------------------+-----------------------+----------+---------+
## | 9 | EDUCATION | 1. 0 | 950 (95.0%) | IIIIIIIIIIIIIIIIIII | 1000 | 0 |
## | | [factor] | 2. 1 | 50 ( 5.0%) | I | (100.0%) | (0.0%) |
## +----+------------------+-----------------------------+---------------------+-----------------------+----------+---------+
## | 10 | RETRAINING | 1. 0 | 903 (90.3%) | IIIIIIIIIIIIIIIIII | 1000 | 0 |
## | | [factor] | 2. 1 | 97 ( 9.7%) | I | (100.0%) | (0.0%) |
## +----+------------------+-----------------------------+---------------------+-----------------------+----------+---------+
## | 11 | AMOUNT | Mean (sd) : 3271.3 (2822.7) | 921 distinct values | : | 1000 | 0 |
## | | [numeric] | min < med < max: | | : . | (100.0%) | (0.0%) |
## | | | 250 < 2319.5 < 18424 | | : : | | |
## | | | IQR (CV) : 2606.8 (0.9) | | : : | | |
## | | | | | : : : : . | | |
## +----+------------------+-----------------------------+---------------------+-----------------------+----------+---------+
## | 12 | SAV_ACCT | 1. 0 | 603 (60.3%) | IIIIIIIIIIII | 1000 | 0 |
## | | [factor] | 2. 1 | 103 (10.3%) | II | (100.0%) | (0.0%) |
## | | | 3. 2 | 63 ( 6.3%) | I | | |
## | | | 4. 3 | 48 ( 4.8%) | | | |
## | | | 5. 4 | 183 (18.3%) | III | | |
## +----+------------------+-----------------------------+---------------------+-----------------------+----------+---------+
## | 13 | EMPLOYMENT | 1. 0 | 62 ( 6.2%) | I | 1000 | 0 |
## | | [factor] | 2. 1 | 172 (17.2%) | III | (100.0%) | (0.0%) |
## | | | 3. 2 | 339 (33.9%) | IIIIII | | |
## | | | 4. 3 | 174 (17.4%) | III | | |
## | | | 5. 4 | 253 (25.3%) | IIIII | | |
## +----+------------------+-----------------------------+---------------------+-----------------------+----------+---------+
## | 14 | INSTALL_RATE | Mean (sd) : 3 (1.1) | 1 : 136 (13.6%) | II | 1000 | 0 |
## | | [numeric] | min < med < max: | 2 : 231 (23.1%) | IIII | (100.0%) | (0.0%) |
## | | | 1 < 3 < 4 | 3 : 157 (15.7%) | III | | |
## | | | IQR (CV) : 2 (0.4) | 4 : 476 (47.6%) | IIIIIIIII | | |
## +----+------------------+-----------------------------+---------------------+-----------------------+----------+---------+
## | 15 | MALE_DIV | 1. 0 | 950 (95.0%) | IIIIIIIIIIIIIIIIIII | 1000 | 0 |
## | | [factor] | 2. 1 | 50 ( 5.0%) | I | (100.0%) | (0.0%) |
## +----+------------------+-----------------------------+---------------------+-----------------------+----------+---------+
## | 16 | MALE_SINGLE | 1. 0 | 452 (45.2%) | IIIIIIIII | 1000 | 0 |
## | | [factor] | 2. 1 | 548 (54.8%) | IIIIIIIIII | (100.0%) | (0.0%) |
## +----+------------------+-----------------------------+---------------------+-----------------------+----------+---------+
## | 17 | MALE_MAR_or_WID | 1. 0 | 908 (90.8%) | IIIIIIIIIIIIIIIIII | 1000 | 0 |
## | | [factor] | 2. 1 | 92 ( 9.2%) | I | (100.0%) | (0.0%) |
## +----+------------------+-----------------------------+---------------------+-----------------------+----------+---------+
## | 18 | CO.APPLICANT | 1. 0 | 959 (95.9%) | IIIIIIIIIIIIIIIIIII | 1000 | 0 |
## | | [factor] | 2. 1 | 41 ( 4.1%) | | (100.0%) | (0.0%) |
## +----+------------------+-----------------------------+---------------------+-----------------------+----------+---------+
## | 19 | GUARANTOR | 1. 0 | 948 (94.8%) | IIIIIIIIIIIIIIIIII | 1000 | 0 |
## | | [factor] | 2. 1 | 52 ( 5.2%) | I | (100.0%) | (0.0%) |
## +----+------------------+-----------------------------+---------------------+-----------------------+----------+---------+
## | 20 | PRESENT_RESIDENT | 1. 1 | 130 (13.0%) | II | 1000 | 0 |
## | | [factor] | 2. 2 | 308 (30.8%) | IIIIII | (100.0%) | (0.0%) |
## | | | 3. 3 | 149 (14.9%) | II | | |
## | | | 4. 4 | 413 (41.3%) | IIIIIIII | | |
## +----+------------------+-----------------------------+---------------------+-----------------------+----------+---------+
## | 21 | REAL_ESTATE | 1. 0 | 718 (71.8%) | IIIIIIIIIIIIII | 1000 | 0 |
## | | [factor] | 2. 1 | 282 (28.2%) | IIIII | (100.0%) | (0.0%) |
## +----+------------------+-----------------------------+---------------------+-----------------------+----------+---------+
## | 22 | PROP_UNKN_NONE | 1. 0 | 846 (84.6%) | IIIIIIIIIIIIIIII | 1000 | 0 |
## | | [factor] | 2. 1 | 154 (15.4%) | III | (100.0%) | (0.0%) |
## +----+------------------+-----------------------------+---------------------+-----------------------+----------+---------+
## | 23 | AGE | Mean (sd) : 35.5 (11.4) | 53 distinct values | : | 1000 | 0 |
## | | [numeric] | min < med < max: | | : . | (100.0%) | (0.0%) |
## | | | 19 < 33 < 75 | | : : : : | | |
## | | | IQR (CV) : 15 (0.3) | | : : : : : | | |
## | | | | | : : : : : : : . . | | |
## +----+------------------+-----------------------------+---------------------+-----------------------+----------+---------+
## | 24 | OTHER_INSTALL | 1. 0 | 814 (81.4%) | IIIIIIIIIIIIIIII | 1000 | 0 |
## | | [factor] | 2. 1 | 186 (18.6%) | III | (100.0%) | (0.0%) |
## +----+------------------+-----------------------------+---------------------+-----------------------+----------+---------+
## | 25 | RENT | 1. 0 | 821 (82.1%) | IIIIIIIIIIIIIIII | 1000 | 0 |
## | | [factor] | 2. 1 | 179 (17.9%) | III | (100.0%) | (0.0%) |
## +----+------------------+-----------------------------+---------------------+-----------------------+----------+---------+
## | 26 | OWN_RES | 1. 0 | 287 (28.7%) | IIIII | 1000 | 0 |
## | | [factor] | 2. 1 | 713 (71.3%) | IIIIIIIIIIIIII | (100.0%) | (0.0%) |
## +----+------------------+-----------------------------+---------------------+-----------------------+----------+---------+
## | 27 | NUM_CREDITS | Mean (sd) : 1.4 (0.6) | 1 : 633 (63.3%) | IIIIIIIIIIII | 1000 | 0 |
## | | [numeric] | min < med < max: | 2 : 333 (33.3%) | IIIIII | (100.0%) | (0.0%) |
## | | | 1 < 1 < 4 | 3 : 28 ( 2.8%) | | | |
## | | | IQR (CV) : 1 (0.4) | 4 : 6 ( 0.6%) | | | |
## +----+------------------+-----------------------------+---------------------+-----------------------+----------+---------+
## | 28 | JOB | 1. 0 | 22 ( 2.2%) | | 1000 | 0 |
## | | [factor] | 2. 1 | 200 (20.0%) | IIII | (100.0%) | (0.0%) |
## | | | 3. 2 | 630 (63.0%) | IIIIIIIIIIII | | |
## | | | 4. 3 | 148 (14.8%) | II | | |
## +----+------------------+-----------------------------+---------------------+-----------------------+----------+---------+
## | 29 | NUM_DEPENDENTS | Min : 1 | 1 : 845 (84.5%) | IIIIIIIIIIIIIIII | 1000 | 0 |
## | | [numeric] | Mean : 1.2 | 2 : 155 (15.5%) | III | (100.0%) | (0.0%) |
## | | | Max : 2 | | | | |
## +----+------------------+-----------------------------+---------------------+-----------------------+----------+---------+
## | 30 | TELEPHONE | 1. 0 | 596 (59.6%) | IIIIIIIIIII | 1000 | 0 |
## | | [factor] | 2. 1 | 404 (40.4%) | IIIIIIII | (100.0%) | (0.0%) |
## +----+------------------+-----------------------------+---------------------+-----------------------+----------+---------+
## | 31 | FOREIGN | 1. 0 | 963 (96.3%) | IIIIIIIIIIIIIIIIIII | 1000 | 0 |
## | | [factor] | 2. 1 | 37 ( 3.7%) | | (100.0%) | (0.0%) |
## +----+------------------+-----------------------------+---------------------+-----------------------+----------+---------+
## | 32 | RESPONSE | 1. 0 | 300 (30.0%) | IIIIII | 1000 | 0 |
## | | [factor] | 2. 1 | 700 (70.0%) | IIIIIIIIIIIIII | (100.0%) | (0.0%) |
## +----+------------------+-----------------------------+---------------------+-----------------------+----------+---------+